I live in North Norfolk about 8 miles from the coast.
Holkham/ Wells next the Sea beach has just been voted the best in the UK, massive expanse of sand and dunes for the kids to play in. You have the pretty town of Wells there (good fish and chips and ice cream), Holkham Hall with big playground, deer in the park etc.
If you base yourself in the area, then you have Sea Life Centre at Hunstanton, seal watching trips a but further along coast. Sandringham royal estate is good with the kids, lots of walks and again a huge playground.
You can travel to Thetford to ride bike, but there are some MTB trails at Sheringham (nice to ride over the cliff on the coastal path).
i would definitely recommend Bewilderwood for your daughter too.
Other than that there is a lot of little zoos, Dinosaur Park etc
This is a good website:
http://www.dayoutwiththekids.co.uk/search.php?county=norfolk
Its only then 40-50 minute drive over to the other side of Norfolk, worth a day in Norwich as it’s an easy city to walk around, with castle etc and maybe have a day on a boat on the Broads too.